First-order satisfiability in Gödel logics: An NP-complete fragment

Authors:
Matthias Baaz;Agata Ciabattoni;Norbert Preining
Affiliations:
Technische Universität Wien, Austria;Technische Universität Wien, Austria;Technische Universität Wien, Austria and Japan Advanced Institute of Science and Technology, Japan
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

Defined over sets of truth values V which are closed subsets of [0,1] containing both 0 and 1, Godel logics G"V are prominent examples of many-valued logics. We investigate a first-order fragment of G"V extended with @D, that is powerful enough to formalize important properties of fuzzy rule-based systems. The satisfiability problem in this fragment is shown to be NP-complete for all G"V, also in the presence of an additional, involutive negation. In contrast to the one-variable case, in the fragment considered, only two infinite-valued Godel logics extended with @D differ w.r.t. satisfiability. Only one of them enjoys the finite model property.